AbyssalMage wrote:First, obviously you didn't notice the LINEAR line from 0-50 (5 Decades)? Guess you skipped over that?

I think Bartlett needs to redo his lecture a bit.

He should start by explaining what a line is, and what it isn't.

And what an exponential function looks like, and how it's different from a line, even though the leftmost part is hard to see when graphed on a linear scale. (Hint: the first five decades are NOT linear.)

I thought those were obvious points but clearly they need explanation. If you don't understand what a line looks like, I'm sure there are others who don't understand it either.

AbyssalMage wrote:First, obviously you didn't notice the LINEAR line from 0-50 (5 Decades)? Guess you skipped over that?

I think Bartlett needs to redo his lecture a bit.

He should start by explaining what a line is, and what it isn't.

And what an exponential function looks like, and how it's different from a line, even though the leftmost part is hard to see when graphed on a linear scale. (Hint: the first five decades are NOT linear.)

I thought those were obvious points but clearly they need explanation. If you don't understand what a line looks like, I'm sure there are others who don't understand it either.

AbyssalMage wrote:
First, obviously you didn't notice the LINEAR line from 0-50 (5 Decades)? Guess you skipped over that?
Second, the Linear Line from 50-60 (A whole DECADE)? Guess you missed that also?

That's only an anomaly of the graph size with the graphic you guys have.

If you averaged out all of those 50 years, to smooth it out, I am going to have to say that it is an exponential curve, AbyssalMage. Not a line.

Going from 50-60 is a sharp upward increase, as you see. Going from 150 to 600 give or take. That is exponential. That's a double in 5 years, and a double in 5 years again. Bartlett math puts that at 14% annual growth per year during those 10 years(70/5 rule).

AbyssalMage wrote:
First, obviously you didn't notice the LINEAR line from 0-50 (5 Decades)? Guess you skipped over that?
Second, the Linear Line from 50-60 (A whole DECADE)? Guess you missed that also?

That's only an anomaly of the graph size with the graphic you guys have.

You (and others who have remarked on it) are correct that the last century, more or less, population growth has been exponential.

Those who claim that before that it must have been linear are also right. Just not for the last century.

If we, very conservatively, put the start of the human race at the end of the last ice age, or about 10000 years ago (which is actually way too short) and we go with the 'doubling every 5 years' figure that is shown in the graphs we should now have at least 2 to the power of 2000 human beings. Those would probably more than fill up the entire volume of the earth.

Ecologies try to keep populations stable and 'bloom' or 'pest' species hint not at a natural state but something out of whack with the predator-prey dynamics in the system (or at a system that regularly resets through major catastrophies).

For most of our history humans have been a prey species and large predators kept us in check.
Later, as we got much better at surviving predators, famine and disease took over the role of large scale killers of humans.
What happened a hundred years ago was the discovery of bacteria and virusses quickly followed by the invention and penecilin and vaccins, which dramatically cut down on the number of deaths each year. Reproduction (i.e. cultural) patterns took a while longer to adjust to the new situation in which not the majority of children died before they were old enough to reproduce themselves, so the population exploded.

By all accounts it looks like the anomaly where we as a species do not have to fear plagues is about to come to an end though, with the appearance of bacteria that are resistant to all available medicines (yes, even to the last ditch medicines that have been kept in reserve the last decade for situations where all else fails).

erianaiel wrote:If we, very conservatively, put the start of the human race at the end of the last ice age, or about 10000 years ago (which is actually way too short) and we go with the 'doubling every 5 years' figure that is shown in the graphs we should now have at least 2 to the power of 2000 human beings. Those would probably more than fill up the entire volume of the earth.

Moderns humans have been around a long longer than 10,000 years.

And the growth rate was not "doubling every 5 years".

Exponential growth can be slow, yet still exponential. It can double every 50 years, 500 years, or 5,000 years, and still be exponential, not linear.

Human populations grow exponentially, until they run out of food.

In the distant past, running out of food meant a tribe of 30 over a large range. Today the number is larger, but the principle is exactly the same.

If you want a modern example of the principle played out in practice, look at the civil war in Rwanda. That is the planet's future at the rate we're going.

Fyyr wrote:That's only an anomaly of the graph size with the graphic you guys have.

That always happens when you plot an exponential curve on a linear scale. Because although the values at the beginning are still growing exponentially, they are tiny compared to the numbers at the end so they look very close to one another.

Which is why, as Bartlett explains, exponential curves are often graphed on a logarithmic scale, because then exponential growth at a constant rate looks like a straight line.

If you graph the DJIA on an logarithmic scale, you get this:

Which is close to a straight line, because the growth of the DJIA is close to an exponential function.

I know you know this, I am explaining it for the others who still don't seem to have a grasp of what a linear function is, and what an exponential function is.

That was in rebuttal to AMs assertion that the DJIA was linear between 1950 and 1960.
It was not, it doubled in 5 years, and doubled again in 5 years. That is 4 times growth in 10 years.
That is not linear.

Not for once do I believe that human population growth from the first human to now was a static figure.
But it had to be exponential, and not linear. Well, maybe for that first human if he or she only had one child live to reproductive age, and then died when his or her grandbaby were born.
That is the only time in human history that growth could have ever been theoretically linear.

I also personally believe that in pre history there were massive human die offs, probably so precipitous to push humans to the brink of extinction.
Note how all, or most of the prehistoric remains found are of species other than homo sapiens. They are almost always branches of hominids, not human, from a common ancestor. That suggests to me that humans, or our direct ancestors, were relatively smaller in number than their competitors.

And easily, today, the maternal death rate would be close to 33% per birth, without medical, midwifery, or nursing. While I don't necessarily think that prehistoric numbers were actually that high, because modern women who now give birth today, would have been selected out by maternal death prehistorically. The logically obvious, if she was never born because her mother died in childbirth, then should could never have died during childbirth. But it had to be high enough for us to invent medicine, midwifery, and nursing(and the other social or tribal traits to nurture mothers and children). Something that our competitors surely never invented.

Tudamorf wrote:In the distant past, running out of food meant a tribe of 30 over a large range.

Do you really think that food availability, prehistorically, was the largest limiting factor to hunter gatherer human population growth?

Equatorial climate was most likely very much like Californian climate is now.
If you and say, 30 of your best hunting and fishing buddies,(and 30 hot gathering chicas) were along any larger river in California by yourself, with no other people around. Do you really think that you would ever run out of food?

Fyyr wrote:Do you really think that food availability, prehistorically, was the largest limiting factor to hunter gatherer human population growth?

Uh, yeah. Hunter-gatherers simply can't live at a high population density. That's how they live today, and that's how archaeological evidence shows they lived in the past.

Unless you'd like to point out a prehistoric hunter-gatherer society of millions.

Fyyr wrote:If you and say, 30 of your best hunting and fishing buddies,(and 30 hot gathering chicas) were along any larger river in California by yourself, with no other people around. Do you really think that you would ever run out of food?

You could feed 30, though you'd need stuff to gather too or you'd die of malnutrition. Maybe in an unusually rich area you could feed 300. But you could never feed a million. That's simply impossible without agriculture.

So yes, so long as females on average can have over two children without dying, food is the limiting factor, and growth will be exponential up to that point.

The Chumash were one of California's largest hunter gatherer societies, estimates at 10,000 are realistic. Pre Columbian.

Most of the northern Californian tribes were much smaller, a few hundred to 1000 or so. Including children. With most of them on the smaller side.

These peoples existed in these smaller groups for 10,000 years or so. Without ever going to a million.

Estimates of the Nisenan and Maidu were 9500. They mainly subsisted on fish and acorns, with other animals and vegetation making up the rest of the diet(IIRC they also had a way of preparing cattails for food). They 'groomed' oak trees and groves to increase production, but it would be a stretch to describe this as agriculture. Possibly pre-agrarian.

I would agree that 10,000 is about the upper limit of hunter gatherer societies living in fertile river and/or ocean areas, and limited by food resources. This is much higher than 30, or 100 or so with women and children. For groups this size in the same areas food would be never-ending abundant, minus some catastrophe, say a volcano, fire, or tidal wave. I don't agree that a group of 30 hunter gatherers were limited by food resources.